T 43. Sackville St W.
Tuesday February 5th
My dear Father.
Salmon’s conic sections, <1> and Mr C R M Talbot <2> on the Newtons lines of the 3rd order <3> are at Lacock and I think in your library. and probably in the book case betw opposite the windows. My mathematics have hardly come to a presentable result. – I have not many mathematical books with me, but I have been attacking several subjects – I hope soon to have something to show. – A simple property of a trapezium which I suppose is well know is this.
[drawing of trapezium]
If you bisect the sides and diagonals of a trapezium, and join eg. fh.I.J. as shown in the figure three lines pass through one point. –
[three more figures, labelled (1), (2), (3)]
This admits of this statement
By the way these lines are all bisect each other. This is another statement. If a figure be [illegible deletion] formed by 4 lines in one plane whether, such figure hav have a reentering angle as figure (2). or whether 2 sides cross as figure. the (3). Ten if you bisect alternate sides and give their centres, these 2 straight lines always bisect each other.
Have you Tates <4> work on quaternion? and is it difficult?
Please thank Monnie <5> for her letter which I have yet to answer.
Your affect son
Charles –
[envelope:]
W. H. Fox Talbot, Esq
13 Great Stuart Street
Edinburgh
Notes:
1. George Salmon (1819–1904), A treatise on conic sections: containing an account of some of the most important modern algebraic and geometric methods (London, Longmans, Brown, Green, Longman, and Roberts, 1863), 4th edition.
2. Christopher Rice Mansel Talbot (1803–1890), immensely wealthy landowner, mathematician & politician; WHFT’s Welsh cousin.
3. Christopher Rice Mansel Talbot, Sir Isaac Newton’s Enumeration of lines of the third order, generation of curves by shadows, organic description of curves, and construction of equations by curves (London, H.G. Bohn, 1860). ‘Enumeratio linearum tertii ordinis’, originally printed as an appendix to the treatise on Optics, and subsequently in the ‘Opuscula’, has not hitherto been published in a separate form.
4. Prof Peter Guthrie Tait (1831–1901), Scottish mathematician.
5. Rosamond Constance ‘Monie’ Talbot (1837–1906), artist & WHFT’s 2nd daughter.